journal of financial economics...we focus, in particular, on the relevance of these mea-sures for a...

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Journal of Financial Economics

Journal of Financial Economics 105 (2012) 18–36

0304-40

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Acharya

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Wang, J

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journal homepage: www.elsevier.com/locate/jfec

Illiquidity or credit deterioration: A study of liquidity in the UScorporate bond market during financial crises$

Nils Friewald a,n, Rainer Jankowitsch a, Marti G. Subrahmanyam b

a WU (Vienna University of Economics and Business), Heiligenstadter Straße 46–48, Vienna 1190, Austriab New York University, Stern School of Business, 44 West Fourth, New York, NY 10012, USA

a r t i c l e i n f o

Article history:

Received 8 October 2010

Received in revised form

11 July 2011

Accepted 8 August 2011Available online 10 February 2012

JEL classification:

G01

G12

G14

Keywords:

Liquidity

Corporate bonds

Financial crisis

OTC markets

5X/$ - see front matter & 2012 Elsevier B.V.

016/j.jfineco.2012.02.001

thank INQUIRE Europe for their support o

for providing us with valuation data. We

, Engelbert Dockner, Peter Feldhutter, Aloi

bert Korajczyk, David Lando, David Lesmond,

ason Wei, and especially the referee, Paul Sch

Schwert, for helpful comments on prior dra

rence participants at the 2009 German Finan

idwest Finance Association, the 2010 Swiss S

Research, the Annual Finance Conference on

te Finance of the Wilfrid Laurier University,

nagement Conference of the National Unive

ernational Risk Management Conference of

e, the Third Erasmus Liquidity Conference

of Management, the 2010 China Internatio

, the WU Gutmann Center Symposium 2

ants at the Copenhagen Business School,

ESSEC, NYU Stern School, the Italian Treasu

or useful comments and suggestions.

esponding author.

ail addresses: [email protected] (N. Friew

[email protected] (R. Jankowitsch),

[email protected] (M.G. Subrahmanyam).

a b s t r a c t

We investigate whether liquidity is an important price factor in the US corporate bond

market. In particular, we focus on whether liquidity effects are more pronounced in

periods of financial crises, especially for bonds with high credit risk, using a unique data

set covering more than 20,000 bonds, between October 2004 and December 2008.

We employ a wide range of liquidity measures and find that liquidity effects account

for approximately 14% of the explained market-wide corporate yield spread changes.

We conclude that the economic impact of the liquidity measures is significantly larger

in periods of crisis, and for speculative grade bonds.

& 2012 Elsevier B.V. All rights reserved.

All rights reserved.

f this project and

also thank Viral

s Geyer, Frank de

Stefan Pichler, Jian

ultz, and the editor,

fts. We are grateful

ce Association, the

ociety for Financial

Recent Advances in

the Fourth Annual

rsity of Singapore,

the University of

of the Rotterdam

nal Conference in

011, and seminar

University of Mel-

ry, and Standard &

ald),

1. Introduction

The global financial crisis had its origins in the USsubprime mortgage market in 2006–2007, but has sincespread to virtually every financial market around theworld. The most important aspect of this crisis, whichsharply distinguishes it from previous crises, is the rapid-ity and degree to which both the liquidity and creditquality of several asset classes deteriorated. While clearlyboth liquidity and credit risk are key determinants ofasset prices, in general, it is important to quantify theirrelative effects and, particularly, how much they changedduring the crisis. It is also relevant to ask if there areinteractions between these factors, and whether theserelations changed substantially in magnitude and qualityfrom prior periods. In this paper, we study liquidityeffects in the US corporate bond market for the periodOctober 2004 to December 2008, including the GM/Ford

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N. Friewald et al. / Journal of Financial Economics 105 (2012) 18–36 19

downgrades and the subprime crisis, using a unique dataset covering basically the whole US corporate bondmarket. We employ a wide range of liquidity measuresto quantify the liquidity effects in corporate bond yieldspreads.Our analysis explores the time-series and cross-sectionalaspects of liquidity for the whole market, as well asvarious important segments, using panel and Fama-MacBeth regressions, respectively.

Most major financial markets, including those forequity, foreign exchange, credit, and commodities, wereseverely affected in terms of price and liquidity in thesubprime crisis. However, the impact has been dispro-portionately felt in the fixed income markets, includingthe markets for collateralized debt obligations (CDO),credit default swaps (CDS), and corporate bonds. Animportant point to note is that these securities are usuallytraded in over-the-counter (OTC) markets, where there isno central market place, or even a clearing house. Indeed,this aspect has come under regulatory scrutiny since thenear collapse of the CDS market, which was an opaqueOTC market. It is the OTC structure of fixed incomemarkets that makes research, especially on liquidityeffects, difficult as traded prices and volumes are notreadily available, and important aspects of the marketscan only be analyzed based on quotations from individualdealers, which are not necessarily representative of themarket as a whole.

US corporate bonds trade in an important OTC market.This market is an ideal laboratory to examine liquidityand credit factors because of the following reasons: First,in contrast to most other OTC markets, detailed transac-tion data are available on prices, volumes, and othermarket variables since 2004, through an effort of theFinancial Industry Regulatory Agency (FINRA), known asthe Trade Reporting and Compliance Engine (TRACE). Thisdatabase aggregates virtually all transactions in the UScorporate bond market, which is unusual for any OTCmarket. Second, the US corporate bond market bore thebrunt of the subprime crisis in terms of credit deterioration,almost to the same extent as the credit derivatives market,to which it is linked by arbitrage and hedging activities.Third, there is considerable variation in credit quality as wellas liquidity in this market, both over time and across bonds,providing researchers with the opportunity to examine thedifferences arising out of changes in liquidity.

For our empirical analysis, we use all traded prices fromTRACE, along with market valuations from Markit, bondcharacteristics from Bloomberg, and credit ratings fromStandard & Poor’s. Our combined data set is perhaps themost comprehensive one of the US corporate bond marketthat has been assembled to date, covering 23,703 bonds and3,261 firms. This data set enables us to study liquidityeffects for virtually the whole bond market, including bondsegments that show very low trading activity.

The main focus of our research in this paper is todetermine the quantitative impact of liquidity factors,while controlling for credit risk, based on credit ratingsand other risk characteristics. In our analysis, we focus onthe yield spread of a corporate bond, defined as its yielddifferential relative to that of a risk-free benchmark of

similar duration. The benchmark could be either theTreasury bond or the swap rate curve.

To measure liquidity, we consider several alternativeproxies for liquidity. We employ bond characteristics thathave been used as liquidity proxies in many studies. Weuse directly observable trading activity variables (e.g., thenumber of trades) and, most important, we employseveral alternative liquidity measures proposed in theliterature, i.e., the Amihud, Roll, zero-return, and pricedispersion measure.

First, we explore the hypothesis that liquidity is pricedin the US corporate bond market. We find that theliquidity proxies account for about 14% of the explainedtime-series variation of the yield spread changes overtime for individual bonds, while controlling for creditquality. Most of the liquidity proxies exhibit statisticallyas well as economically significant results. While thetrading activity variables are important in explaining thebond yield spread changes, the liquidity measures exhibiteven stronger effects in terms of economic impact. Inparticular, measures estimating trading costs based ontransaction data show the strongest effects.

Second, our main research question is whether theeffect of liquidity is stronger in times of crises. Ourhypothesis is that in crises, when capital constraintsbecome binding and inventory holding costs and searchcosts rise dramatically, liquidity effects are more pro-nounced. Therefore, we analyze credit and liquidityeffects for three different regimes during our sampleperiod, i.e., the GM/Ford crisis, the subprime crisis, andthe period in between, when market conditions weremore normal. Based on time-series analysis, we find thatthe effect of the liquidity measures is far stronger in boththe GM/Ford crisis and the subprime crisis: the economicsignificance of the liquidity proxies increased by 30% inthe GM/Ford crisis compared to the normal period, andmore than doubled in the subprime crisis. We alsoexamine the cross-sectional behavior of the yield spreadusing Fama-MacBeth regressions in the three differenttime periods. In general, the cross-sectional results paint apicture similar to the time-series analysis. Moreover, wefind in the cross-section that time-invariant bond char-acteristics, e.g., amount issued, show significant effectsas well.

Third, we analyze the interaction between credit andliquidity risk. We expect to find higher liquidity in theinvestment grade sector if liquidity concerns cause inves-tors to abandon the junk bond market in favor of invest-ment grade bonds in a flight-to-quality. We presentdescriptive statistics providing evidence for a flight-to-quality during financial distress and the regression ana-lysis indeed shows lower liquidity for speculative gradebonds as well as a stronger reaction to changes inliquidity. In general, these results indicate that the liquid-ity component is far more important in explaining thechange in the yield spread for bonds with high credit risk.

The remainder of the paper is organized as follows: wepresent a survey of the relevant literature in Section 2 ofthe paper, focusing mainly on papers relating to liquidityeffects in corporate bond markets. Section 3 discusses thehypotheses being tested in the paper and the economic

N. Friewald et al. / Journal of Financial Economics 105 (2012) 18–3620

motivation behind them. In Section 4, we explain, indetail, the composition of our data set and the filtersand matching procedures we employ in combining datafrom four different data sources. Section 5 discusses thealternative measures of liquidity that have been proposedand used in the literature and their pros and cons.We focus, in particular, on the relevance of these mea-sures for a relatively illiquid OTC market. In Section 6 weoutline the methodology. Section 7 presents the time-series results, based on panel regressions, and the resultsfor the cross-sectional analysis based on the Fama-Mac-Beth procedure, used to test our hypotheses. Section 8concludes.

2. Literature survey

The academic literature on liquidity effects on assetprices is vast. An early paper was by Amihud andMendelson (1986), who first made the conceptual argu-ment that transaction costs result in liquidity premiumsin asset prices in equilibrium, due to different tradinghorizons of investors. This conclusion has been extendedand modified in different directions and also been testedin a host of asset markets. This literature, focusing mainlyon equity markets, is surveyed by Amihud, Mendelson,and Pedersen (2006). In the context of OTC markets,Duffie, Garleanu, and Pedersen (2007) show that transac-tion costs are driven by search frictions, inventoryholding costs, and bargaining power in this particularmarket structure. A related argument is presented inJankowitsch, Nashikkar, and Subrahmanyam (2011). In arecent paper, Acharya, Amihud, and Bharath (2009) arguethat these frictions change over time and are higher intimes of financial crises, due to binding capital constraintsand increased holding and search costs.

The literature on credit risk modeling provides evi-dence of liquidity effects in the corporate bond marketand shows that risk-free interest rates and credit risk arenot the only factors that drive corporate bond prices. Thisresult has been established based on reduced-form mod-els (see, for example, Longstaff, Mithal, and Neis, 2005;Nashikkar, Subrahmanyam, and Mahanti, 2011), andstructural models (see, for example, Huang and Huang,2003), i.e., neither credit risk measured by the prices ofCDS contracts nor asset value information from the equitymarket, can fully explain corporate bond yields.

Several authors study the impact of liquidity, based oncorporate bond yields or yield spreads over a risk-freebenchmark. Most of these papers rely on indirect proxiesbased on bond characteristics such as the coupon, age,amount issued, industry, and bond covenants; somepapers additionally use market-related proxies based ontrading activity such as trade volume, number of trades,number of dealers, and the bid-ask spread, see, e.g., Elton,Gruber, Agrawal, and Mann (2001), Collin-Dufresne,Goldstein, and Martin (2001), Perraudin and Taylor(2003), Eom, Helwege, and Huang (2004), Liu, Longstaff,and Mandell (2004), Houweling, Mentink, and Vorst(2005), Longstaff, Mithal, and Neis (2005), De Jong andDriessen (2006), Edwards, Harris, and Piwowar (2007),and Acharya, Amihud, and Bharath (2009). Essentially, all

these papers find that liquidity is priced in bond yields.However, they find different magnitudes and varyingimportance of these basic liquidity proxies, but mostlyat the market-wide level.

In the more recent literature, several alternative liquid-

ity measures that are estimators of transaction costs,market impact, or turnover, have been proposed andapplied to analyze liquidity in the corporate bond marketat the level of individual bonds. The Roll measure (see Roll,1984; Bao, Pan, and Wang, 2011) interprets the subse-quent prices as arising from the ‘‘bid–ask bounce’’: thus,the autocovariance in price changes provides a simpleliquidity measure. A similar idea to measure transactioncosts is proposed and implemented in the LOT measure

proposed by Lesmond, Ogden, and Trzcinka (1999). TheAmihud measure (see Amihud, 2002) relates the priceimpact of a trade to the trade volume. Trading activityitself is used in the zero-return measure based on thenumber of unchanged sequential prices and the no-trade

measure based on time periods without trading activity(see, e.g., Chen, Lesmond, and Wei, 2007). Mahanti,Nashikkar, Subrahmanyam, Chacko, and Mallik (2008)propose another measure known as latent liquidity thatis based on the institutional holdings of corporate bonds,which can be used even in the absence of transactiondata. Jankowitsch, Nashikkar, and Subrahmanyam (2011)develop the price dispersion measure, which is based onthe dispersion of market transaction prices of an assetaround its consensus valuation by market participants.

Most of the early papers on bond market liquidity arebased only on quotation data as reasonably completetransaction data were not available until a few yearsago. However, some papers use restricted samples of thetransaction data for certain parts of the corporate bondmarket to analyze liquidity, including Chakravarty andSarkar (1999), Hong and Warga (2000), Schultz (2001),and Hotchkiss and Ronen (2002). Many more researchersfocused on the issue of liquidity in the corporate bondmarket since the TRACE data on US corporate bond trans-actions started to become available in 2002. This newsource of bond price information allows researchers toanalyze many different aspects of the US corporate bondmarket; see, e.g., Edwards, Harris, and Piwowar (2007),Goldstein and Hotchkiss (2007), Mahanti, Nashikkar,Subrahmanyam, Chacko, and Mallik (2008), Ronen andZhou (2009), Nashikkar, Subrahmanyam, and Mahanti(2011), Lin, Wang, and Wu (2011), and Jankowitsch,Nashikkar, and Subrahmanyam (2011).

It is especially interesting to examine how liquidityaffects the corporate bond market in times of financialcrisis. While much of the research on the current financialcrisis is probably in progress, two recent papers doprovide some early evidence on the impact of liquidityin the US corporate bond market. These include Bao, Pan,and Wang (2011) and Dick-Nielsen, Feldhutter, and Lando(2012).

Bao, Pan, and Wang (2011) use the TRACE data toconstruct the Roll measure as a proxy for liquidity. Using asample of around 1,000 bonds that existed prior toOctober 2004, they show that illiquidity measured bythe Roll measure is quite significant in this market and


much larger than would be predicted by the bid–askbounce. They also show that their measure exhibitscommonality across bonds, which tends to go up duringperiods of market crisis. Further, they relate the Rollmeasure to bond yield spreads in a cross-sectional regres-sion setup and provide evidence that part of the yieldspread differences across bonds is due to illiquidity.

Dick-Nielsen, Feldhutter, and Lando (2012) combinethe TRACE data using straight bullet bonds (around 4,000bonds), with accounting data and equity volatility, asproxies for credit risk. They use a panel regression basedon quarterly data to study the effects of five differentliquidity measures and the defined credit risk variables. Ingeneral, they find a significant effect of liquidity, whichincreased with the onset of the subprime crisis. However,their multivariate regression results show somewhatmixed results for different rating classes.

There are several important differences between theseprior papers and our own research in this paper. First, weemploy a much larger data set on transaction data on UScorporate bonds than any prior papers, as our sample of23,703 bonds basically covers the whole traded market.This is a major difference even compared with the recentwork of Bao, Pan, and Wang (2011) and Dick-Nielsen,Feldhutter, and Lando (2012), who focus only on a certain,generally the more liquid, subsegment of the market.Second, our research explicitly covers two crisis periods,which are analyzed separately: the broader subprime crisisand the earlier, GM/Ford crisis, which affected particularsegments of the US corporate bond market. We contrastthe behavior of liquidity and its pricing in bond yieldspreads during periods of crisis with more normal periodsand analyze the interaction of credit and liquidity risk.Third, we include the additional information on the mar-ket’s consensus valuation of bonds provided by Markit.These data permit us to estimate the price dispersionmeasure for the bonds in our sample and, thus, includean important additional measure of transaction costs. Thisliquidity proxy is particularly relevant for our researchquestion, as transaction cost measures appear to be espe-cially important in explaining liquidity in OTC markets.

3. Hypotheses

In this section, we provide an overview of the researchquestions we pose and the hypotheses we test in ourresearch. Our approach is to examine the validity ofspecific arguments regarding the effect of liquidity inthe US corporate bond market.

H1: Liquidity is an important price factor in the US

corporate bond market.

As argued by Amihud and Mendelson (1986), investorswith different trading horizons have different expectedreturns, after taking into account the transactions costs theywill incur over their respective horizons. This phenomenontranslates into a clientele effect (for securities in positivenet supply) by which the more illiquid assets are cheaperand are held by investors with longer horizons relative totheir liquid counterparts, which are held by those withshorter horizons. Duffie, Garleanu, and Pedersen (2007) and

Jankowitsch, Nashikkar, and Subrahmanyam (2011) arguethat in OTC markets the liquidity premium is driven bytransaction costs due to search frictions, inventory holdingcosts, and bargaining power. In the corporate bond marketcontext, these frictions are reflected in the bond prices,whereby liquid bonds earn a lower expected return thanilliquid bonds which are similar on other dimensions, suchas bond features and risk characteristics.

The US corporate bond market is especially interestingin this respect, as liquidity differences across individualbonds seem to be rather pronounced: very few bonds aretraded frequently, while most other bonds are hardly evertraded at all (see Mahanti, Nashikkar, Subrahmanyam,Chacko, and Mallik, 2008 for details of a cross-sectionalcomparison for the US corporate bond market). Moreover,trading in the US corporate bond market involves muchhigher transaction costs compared to related marketssuch as the stock market. Thus, we would expect asignificant liquidity premium, as argued in Amihud andMendelson (1986), and expect that our liquidity proxiescan explain a significant part of bond yield spreads. Ouraim is to quantify these liquidity effects as a priced factor.

H2: Liquidity effects are more important in periods of

financial distress.

The liquidity premium in the corporate bond market canbe expected to change over time depending on marketconditions, especially during a financial crisis. Several argu-ments have been proposed in the literature regarding thebehavior of agents in a crisis. For example, Duffie, Garleanu,and Pedersen (2007) propose that liquidity is more impor-tant in crisis periods, since inventory holding costs andsearch costs are higher, and also asymmetric information isa more important issue. Acharya, Amihud, and Bharath(2009) provide empirical support for this hypothesis arguingthat banks face more stringent capital requirements whenthey hold illiquid assets and could find it more difficult toaccess liquidity during a crisis. Moreover, a greater propor-tion of investors could have shorter horizons in a crisis. Forexample, bond mutual funds and hedge funds could face thepossibility of redemptions or are forced to meet value-at-risk requirements and margin calls and, therefore, wish tohold more liquid assets to address this eventuality; see, e.g.,Sadka (2010). Individual investors could shift more of theirportfolios from illiquid to liquid assets as they turn morerisk averse. For all these reasons, the gap in pricing betweenliquid and illiquid bonds, that are otherwise similar, maywiden, resulting in a higher liquidity premium.

Thus, the second and main research question of thispaper is whether the effect of liquidity is stronger duringtimes of financial crises. We expect a particularly strongeffect in the subprime crisis, when capital constraintsbecame binding and inventory holding costs and searchcosts rose dramatically for all market participants.

H3: Liquidity effects are more important for bonds with

high credit risk.

We study whether a bond’s credit rating is related toliquidity effects by focusing on the difference betweeninvestment grade and speculative grade bonds. Acharya,Amihud, and Bharath (2009) show that liquidity is


substantially different between investment grade andspeculative grade bonds using a regime switching model.They argue that in periods of financial crisis, all bondprices decline due to an increase of illiquidity. At the sametime, a flight-to-quality effect is expected, which leads tolower price reactions among investment grade bonds.Chen, Lesmond, and Wei (2007) also provide empiricalsupport for this argument. Thus, we expect strongerliquidity effects for speculative grade bonds and to findflight-to-quality effects in periods of crisis.

4. Data description

In this section, we present the unique data set we haveat hand for this liquidity study covering basically thewhole US corporate bond market. Our data are drawnfrom several different sources:

1.

and

wh

To

sug

Transaction data from the Trade Reporting and Com-pliance Engine (TRACE).

2.
Consensus market valuations from Markit. 3. Credit ratings from Standard & Poor’s. 4. Bond characteristics from Bloomberg. 5. Treasury and swap data from Bloomberg.
Our time period starts with the date when TRACE wasfully implemented on October 1, 2004, and covers theperiod until December 31, 2008. TRACE provides detailedinformation about all transactions in the US corporate bondmarket, i.e., the actual trade price, the yield based on thisprice, as well as the trade volume measured in US dollarsfor each transaction.1 Phase I of TRACE was launched by theFinancial Industry Regulatory Agency (FINRA) in July 2002,with the aim of improving transparency in the US corporatebond market. This phase covered only the larger andgenerally higher credit quality issues. Phase II expandedthe coverage and dissemination of information to smallerinvestment grade issues. Since the final Phase III was imple-mented on October 1, 2004, transactions of essentially allUS corporate bonds have been reported. Hence, the TRACEdatabase has been reasonably complete since its finalimplementation. This data source is almost unique for anOTC market, since in many other cases, price informationusually must be obtained either from an individual dealer’strading book, which provides a very limited view of themarket, or by using bid–ask quotations instead. In the UScorporate bond market, reporting of any transaction toTRACE is obligatory for broker-dealers and follows a set ofrules approved by the Securities and Exchange Commission(SEC), whereby all transactions must be reported within atime frame of 15 minutes.

We use the filters proposed by Dick-Nielsen (2009) forthe TRACE data to eliminate potentially erroneous datapoints.2 In addition, we follow Edwards, Harris, and

1 The reported trade volume is capped at $1 million for high yield

unrated bonds and at $5 million for investment grade bonds.2 As pointed out by Dick-Nielsen (2009), care should be exercised

en accounting for order cancelations or corrections in the TRACE data.

mitigate the errors that result from these issues, Dick-Nielsen (2009)

gests that the trade data need to be ‘‘cleaned up’’ using error filters.

Piwowar (2007) and apply a median filter and a reversal

filter to eliminate further potential data errors. While themedian filter identifies potential outliers in reportedprices within a certain time period, the reversal filteridentifies unusual price movements.3 Eliminating anypotential errors in the reported transactions reduces thenumber of reported trades by roughly 5.5% to 23.5 milliontrades. This results in a TRACE data sample consisting of34,822 bonds from 4,631 issuers.

An important additional source for the market’s valua-tion of a bond is obtained from Markit Group Limited, aleading data provider, specialized in security and deriva-tives pricing. One of its services is to gather, validate, anddistribute end-of-day composite bond prices from dealerpolls. Up to 30 contributors provide data from their booksof record and from feeds to automated trading systems(see Markit Group Limited, 2006). These reported valua-tions are averaged for each bond after eliminating out-liers, using their proprietary methodology. Hence, thisprice information can be considered as a market-wideaverage of a particular bond price, reflecting the marketconsensus. The Markit valuations are used by manyfinancial institutions to mark their portfolios to marketand have credibility among practitioners. In total, we have5,522,735 Markit quotes, covering 28,145 bonds in ourdatabase.

To control for default risk, we use credit ratings fromStandard & Poor’s (S&P). We focus on long-term, issuecredit ratings as the market’s current judgment of theobligor’s creditworthiness with respect to a specificfinancial obligation. It should be noted, that in ourdescriptive statistics of the rating variable, we assigninteger numbers to ratings, i.e., AAA¼1, AAþ¼2, etc., tomeasure the ‘‘average’’ rating of certain groups of bondsor time periods. Our time period contains 25,464 bonds,which have at least one S&P credit rating each. Note thatcredit risk could be measured using alternativeapproaches. Two prominent examples come to mind:using CDS spreads in the context of a reduced-form creditrisk model, as in Longstaff, Mithal, and Neis (2005) andNashikkar, Subrahmanyam, and Mahanti (2011), or usingaccounting-based and equity-related data in a structuralmodel context, as in Huang and Huang (2003). We do notincorporate such proxies as this information is generallyonly available for a very small (presumably more liquid)segment of the market and our intention is to explicitlyanalyze liquidity effects for the whole market. In addition,the impact of the liquidity on these data inputs wouldalso have to be taken into account, rendering the analysisfar more complex, and hence, prone to additional error.This issue is particularly true during periods of crisiswhen liquidity and counterparty risk considerations areexacerbated in the pricing of CDS as well as equity con-tracts. Hence, we apply the more parsimonious approachof using only the credit ratings, with their admitted

3 The median filter eliminates any transaction where the price

deviates by more than 10% from the daily median or from a nine-

trading-day median centered at the trading day. The reversal filter

eliminates any transaction with an absolute price change deviating from

the lead, lag, and average lead/lag price change by at least 10%.


shortcomings, in terms of their own error and failure toanticipate changes in credit risk.

For each of the bonds available in TRACE, we addition-ally obtain bond characteristics from Bloomberg. Thesebond characteristics include the issue date, maturity, age,coupon, amount issued, industry sector, and bond cove-nants. Most of these characteristics have been consideredas simple liquidity proxies by previous studies. Further-more, we use swap rates and Treasury rates for variousmaturities retrieved from Bloomberg as the benchmarkfor the risk-free interest rate curve to compute thecorporate bond yield spreads.

Given these data sets, we generate a sample that isrepresentative of the whole market by merging the dailytrade observations from TRACE with end-of-day Markit-quotations, the available S&P ratings, and the bondcharacteristics. This sample covers 23,703 bonds of3,261 firms. On average per day, we observe 5,423 tradedbonds, 21,254 trades, and $7.563 billion in volume. Thus,our panel data set covers approximately 80% of the overalltrading activity in the US corporate bond market. We findthat the market coverage is at this high level throughoutthe observation period and, hence, is highly representa-tive of the whole US corporate bond market includingbonds with very low trading activity, which is a majordifference compared to most other studies. Nevertheless,a considerable number of bonds is traded only very rarely.However, data limitations caused by this lack of tradingactivity should actually bias us against finding any clearliquidity effects at all.

5. Liquidity proxies

This section presents the various liquidity proxies thatwe use in the regression analysis as explanatory variables.A number of liquidity proxies have been proposed in theliterature (see Section 2) which are not all equally viable,given the challenges of obtaining detailed and sufficientlyfrequent data in the relatively illiquid corporate bondmarket. Our data set allows us to compare the efficiencyof most of these proposed proxies in this empiricalstudy. We classify the available proxies into three groups:bond characteristics, trading activity variables, and liquidity

measures.Bond characteristics, such as the amount issued, are

simple liquidity proxies which provide a rough indicationabout the potential liquidity of a bond. Trading activityvariables, such as the number of trades, provide bond-specific information based on transaction data. Liquiditymeasures, such as the price dispersion and Amihudmeasure, are alternative estimators of transaction costsor market impact.4

4 We are aware that many studies without access to transaction

data use the quoted bid–ask spread as a liquidity proxy. However, bid–

ask spreads are, in general, only available for a small subsample

representing the relatively larger issues. In a robustness check we find

that bid–ask spreads from Bloomberg are of minor importance once

transaction-based measures are considered, in the empirical specifica-

tions we investigate below. These results are not reported in this paper,

but are available from the authors upon request.

All these liquidity proxies can either be calculated on adaily basis, if price information is observable for a parti-cular bond, or are time-invariant (e.g., coupon), or changelinearly with time (e.g., age). In the following subsections,we present the definitions of the various liquidity proxiesthat we use in our analysis and discuss the details of theircomputation.

5.1. Bond characteristics

The bond characteristics we consider as liquidityproxies are the amount issued, coupon, maturity, and age.These proxies, while admittedly crude measures, makeintuitive sense. In general, we expect bonds with a largeramount issued to be more liquid and bonds with a largercoupon to be less liquid.5 Bonds with long maturities(over 10 years) are generally considered to be less liquidsince they are often bought by ‘‘buy-and-hold’’ investors,who trade infrequently. Similarly, we expect recentlyissued (on-the-run) bonds to be more liquid. We considerthese measures to be important only for our cross-sectional analysis, as most of these are either constant(e.g., coupon) or change linearly (e.g., maturity) over time.

5.2. Trading activity variables

A bond’s trading activity provides information aboutliquidity. In this sense, higher trading activity generallyindicates higher liquidity. We consider the followingtrading activity variables: number of trades, trade volume,and trading interval. We compute the number of tradesand the trade volume of a particular bond on each dayfrom the trading information given by TRACE. The tradinginterval is the elapsed time (measured in days) since thelast day a given bond was traded. Longer trade intervalsindicate less trading activity and, thus, lower liquidity.Therefore, we expect liquidity to be higher for bonds withshorter time intervals between trading days.

5.3. Liquidity measures

5.3.1. Amihud measure

This liquidity proxy is a well-known measure origin-ally proposed for the equity market by Amihud (2002),which is conceptually based on Kyle (1985). It relates theprice impact of trades, i.e., the price change measured as areturn, to the trade volume measured in US dollars. TheAmihud measure at day t for a certain bond over aparticular time period with Nt observed returns is definedas the average ratio between the absolute value of thesereturns rj and its trading volumes vj, i.e.,

Amihudt ¼1

Nt

XNt

j ¼ 1

9rj9vj: ð1Þ

5 Note that the coupon per se is rather a crude proxy for credit risk.

Once we adjust for credit risk (e.g., by using ratings), bonds with

different coupons but with identical credit risk exhibit different levels

of liquidity. However, as we are certainly not able to perfectly adjust for

credit risk, the coupon cannot be viewed as a pure liquidity proxy.

(footnote continued)

Roll measure) and not using these observations at all. Neither of these

changes affects the qualitative nature of our results.


A larger Amihud measure implies that trading a bondcauses its price to move more in response to a givenvolume of trading, in turn, reflecting lower liquidity. Weuse the daily volume-weighted average TRACE prices togenerate the returns rj and calculate the Amihud measureon a day-by-day basis.

5.3.2. Price dispersion measure

A new liquidity measure recently introduced for theOTC market is the price dispersion measure of Jankowitsch,Nashikkar, and Subrahmanyam (2011). This measure isbased on the dispersion of traded prices around themarket-wide consensus valuation. A low dispersion aroundthe valuation indicates that the bond can be bought closeto its fair value and, therefore, represents low trading costsand high liquidity, whereas high dispersion implies hightransaction costs, and hence, low liquidity. This measure isderived from a market microstructure model and showsthat price dispersion is the result of market frictions suchas inventory risk for dealers and search costs for investors.It presents a direct estimate of trading costs based ontransaction data. As in Jankowitsch, Nashikkar, andSubrahmanyam (2011), the traded prices are obtainedfrom TRACE and the market valuations from Markit. Theprice dispersion measure is defined as the root meansquared difference between the traded prices and therespective market-wide valuation weighted by volume,i.e., for each day t and a particular bond, it is given by

Price dispersiont ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1PKt

k ¼ 1 vk

XKt

k ¼ 1

ðpk�mtÞ2vk

vuut , ð2Þ

where pk and vk represent the Kt observed traded pricesand their trade volumes on date t and mt is the market-wide valuation for that day. Hence, the price dispersionindicates the potential transaction cost for a trade.

5.3.3. Roll measure

This measure developed by Roll (1984) shows that,under certain assumptions, adjacent price movements canbe interpreted as a bid–ask bounce which, therefore,allows us to estimate the effective bid–ask spread. Thisbid-ask bounce results in transitory price movements thatare serially negatively correlated and the strength of thiscovariation is a proxy for the round-trip costs for aparticular bond, and hence, a measure of liquidity. Moreprecisely, the Roll measure is defined as

Rollt ¼ 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�CovðDpt ,Dpt�1Þ

q, ð3Þ

where Dpt is the change in prices from t�1 to t. Wecompute the Roll measure based on the daily volume-weighted bond prices pt from the TRACE data set, wherewe use a rolling window of 60 days and require at leasteight observations to determine the covariance.6

6 If positive covariances occur, we set the Roll measure to zero. Since

we interpret the Roll measure as a transaction cost metric, we think it is

quite reasonable to bound this measure at zero. However, we also

compared the results with two alternatives: preserving the sign in the

spirit of Roll (1984) (i.e., positive covariance translates into a negative

5.3.4. Zero-return measure

The zero-return measure indicates whether weobserve a zero price movement between trading days.The zero-return measure is set to one, if we find anunchanged price, and is set to zero, otherwise. Bondprices that stay constant over long time periods are likelyto be less liquid, as the information could be stale.Obviously, such a measure can only be based on pricequotations or valuations, such as Markit quotes in ourcase. Constant price information in these data sourcesreveal illiquidity as unchanged quotations could indicatean incomplete coverage of the bond.

6. Methodology

This section outlines our general approach to measur-ing the impact of liquidity and credit risk on pricing in theUS corporate bond market. We present here our defini-tions of the bond yield spread and define the subperiodsof interest to test our hypotheses about financial crises.We then present the specifications for our panel dataregressions to explore the time-series properties, and theFama-MacBeth regressions to explore the cross-sectionalproperties of our data. We use these specifications tostudy market-wide liquidity effects and analyze subseg-ments of the market, where we compare investmentgrade and speculative grade bonds.

6.1. Bond yield spread

The dependent variable in our setup is the corporatebond yield spread, represented by the yield differentialrelative to that of a risk-free benchmark. We define thisbenchmark as the yield of a risk-free zero-coupon bondwith a maturity equal to the duration of the corporatebond. We compute this duration based on the reportedyield in the TRACE database and the corporate bond’s cashflow structure. Note that we do not incorporate adjust-ments for optionalities or covenants included in the bondstructure to determine the duration. Overall, yield spreadsbased on this duration adjustment can be considered as aproxy for the zero-coupon yield spread taken from a morecomplete pricing model.7

We use both the Treasury yield curve and the swapcurve as risk-free benchmarks to calculate the bond yieldspreads. We find that the general structure of the result-ing yield spread is basically identical for both bench-marks. However, as expected, the yield spread based onthe swap curve is shifted downwards compared to thespread based on the Treasury curve, indicating that theswap curve represents market participants with AA

7 Given the complexity of these models and the limited information

available for their calibration, we presume that the resulting zero-

coupon yield spread would not improve the economic interpretation

of our results, in general. To test this assumption, we have employed

regression analyses for a subsample of straight coupon, bullet bonds

without any option features. For this subsample, we find similar results,

confirming our conjecture.

Fig. 1. Timeline showing important events in the US corporate bond market, since March 2005. Based on these events, we identified three different

regimes: the GM/Ford crisis between March 2005 and January 2006, the normal period from February 2006 to June 2007, with no exceptional events, and

the subprime crisis that started in July 2007.


ratings with greater credit risk, while the Treasury curverepresents lower credit risk. We conduct all our regres-sion analysis on both spread series; however, as theresults are basically identical, we report only the resultsfor the spreads against the Treasury benchmark in theempirical results section.

We calculate the bond yield spread for every priceobservation in the TRACE data set. Thus, we can havemore than one spread observation for a given bond on aparticular day, since there can be multiple trades for thebond on that day. Hence, to get a single value for the yieldspread for each day, we estimate the bond spread fromthe individual observations by calculating a volume-weighted average for the day, i.e., we implicitly assumethat the spread information is reflected more strongly inlarge trades.

6.2. Subperiods of interest

We are interested in how the explanatory power of theindependent variables differs in financial crises comparedto normal market environments. Therefore, we define thefollowing three subperiods: The GM/Ford crisis (March2005–January 2006) when a segment of the corporatebond market was affected, the subprime crisis (July 2007–December 2008), which was much more pervasive acrossthe corporate bond market, and the normal period inbetween (February 2006–June 2007). We choose the startand end dates of the subperiods based on exceptionalevents that are believed to have affected market condi-tions (see Fig. 1).8

6.3. Panel data regression

We rely on a panel data regression approach to analyzebond yield spread changes. We use first differences, aswe observe that yield spreads are integrated. Since weobserve autocorrelated yield spread changes, we add one

8 Alternative definitions of these subperiods could have been used.

Therefore, as a stability test, we varied the start and end dates of the

subperiods by up to one month. However, we find similar results, and

hence, report only results for the three subperiods defined above.

autoregressive parameter to our specifications.9 Of course,in this difference specification, the static bond character-istic variables drop out. Thus, our panel consists of thepooled time-series of the first differences of the bondyield spread as the dependent variable and the tradingactivity variables and liquidity measures as the explana-tory variables. Furthermore, we add changes in ratingclass dummies to the regression to consider credit risk-related effects on the yield spread:

DðYield spreadÞi,t ¼ a0þa1 �DðYield spreadÞi,t�1

þa2 � DðTrading activity variablesÞi,tþa3 � DðLiquidity measuresÞi,tþa4 � DðRating dummiesÞi,tþEi,t : ð4Þ

Our basic time-series data are at a daily frequency.However, because of computational restrictions due tothe large sample size, we create weekly averages of allvariables from the daily data for each bond. Thus, all thetime-series regression results presented in the empiricalresults section below are based on weekly data. Note thatwe use logarithmic values of the traded volume in theregressions, as is common practice.

6.4. Fama-MacBeth cross-sectional regression

These regressions are in levels rather than in changesand, therefore, allow a cross-sectional analysis. In parti-cular, we can test for the importance of static bondcharacteristics in explaining the cross-sectional differ-ences in yield spread. The regressions are performed withthe following structure:

ðYield spreadÞi,t ¼ a0þa1 � ðBond characteristicsÞi,tþa2 � ðTrading activity variablesÞi,tþa3 � ðLiquidity measuresÞi,tþa4 � ðRating dummiesÞi,tþEi,t : ð5Þ

We run this regression based on weekly averagesfrom the daily data of all variables. Thus, we have the

9 We investigated alternative specifications of the time-series

model, including different lags of the autoregressive parameters, and

find that the results are very similar for these specifications.

Table 1This table reports the cross-sectional descriptives statistics (5th, 25th, 50th, 75th, and 95th quantiles, mean, and standard deviation) for the yield spread,

credit rating, bond characteristics, and liquidity proxies. The corporate bond yield spread is measured relative to the US Treasury bond yield curve and

given in percentage points. We use credit ratings from Standard & Poor’s where we assign integer numbers to ratings, i.e., AAA¼1, AAþ¼2, etc., to

measure the average rating. The liquidity proxies are classified into three groups: bond characteristics (amount issued, coupon, maturity, and age),

trading activity variables (traded volume, number of trades, and time interval between trades), and liquidity measures (Amihud, price dispersion, Roll,

and zero-return measure). For time-varying variables, the statistics are first averaged across time for each individual bond. The data set consists of 23,703

US corporate bonds traded over the period October 2004 to December 2008.

Q0:05 Q0:25 Q0:50 Q0:75 Q0:95 Mean Std. dev.

Yield spread (%) 0.52 1.17 1.92 3.67 7.67 2.87 2.95

Rating 1.30 5.00 7.03 11.50 15.46 8.00 4.14

Bond characteristics Amount issued (bln) 0.00 0.01 0.20 0.40 1.25 0.32 0.50

Coupon (%) 3.03 5.00 5.97 7.00 9.13 5.98 1.87

Maturity (yr) 0.45 1.83 5.20 9.74 24.87 7.62 7.63

Age (yr) 0.47 1.52 2.77 4.53 10.36 3.80 3.61

Trading activity variables Volume (mln) 0.02 0.05 0.39 1.74 5.23 1.35 2.53

Trades 1.45 2.00 2.46 3.25 8.44 3.47 4.50

Trading interval (dy) 1.50 2.72 4.48 5.72 7.80 4.46 2.18

Liquidity measures Amihud (bp per mln) 0.68 9.99 38.33 103.01 260.68 78.38 137.21

Price dispersion (bp) 1.69 16.08 33.64 58.00 106.84 41.53 35.56

Roll (bp) 24.48 82.99 155.98 259.69 420.86 185.12 144.69

Zero-return (%) 0.00 0.00 0.01 0.02 0.16 0.03 0.08


cross-sectional regression result for each week and weuse the Fama-MacBeth procedure to report the regressionparameters and t-statistics. We present the results of thisprocedure for the subperiods defined earlier. Thisapproach allows us to analyze liquidity effects in timesof regular market conditions and financial crises, acrossbonds. Again, we use logarithmic values of the tradedvolume and the amount issued in the regressions.

7. Results

7.1. Descriptive statistics

This section provides summary statistics for the UScorporate bond market based on our matched datasample of 23,703 bonds for the period October 2004 toDecember 2008 (see Section 4). Table 1 reports the cross-sectional variation of the main variables used in ourempirical analysis, i.e., the yield spread, the credit rating,and the liquidity proxies (bond characteristics, tradingactivity variables, and liquidity measures). For time-vary-ing explanatory variables, the statistics are computed asthe time averages for each individual bond. The tablereports the 5th, 25th, 50th, 75th, and 95th percentiles, aswell as the mean and standard deviation of each variable.It provides an aggregate picture of the substantial cross-sectional variation of the variables.

The yield spread between the 5th and 95th percentilesranges from 52 to 767 basis points (bp) with a mean of287 bp. Part of this enormous variation is obviously due tocredit risk given that our sample contains bonds withcredit ratings all the way from AAA (¼1) to C (¼21). Theaverage credit rating is roughly eight which correspondsto BBBþ and a standard deviation of approximately fourrating notches.

As is to be expected, there is a reasonable variation inthe bond characteristics of amount issued, coupon,

maturity, and age across bonds, e.g., the amount issuedvaries from just below $5 million to $1.25 billion betweenthe 5th and 95th percentiles. Regarding trading activityvariables, we find that the average frequency of bondtrading is every 4.5 days. For a bond that is traded on aparticular day, we observe an average of 3.5 trades withan average trade size of roughly $1.4 million dollars, withsubstantial cross-sectional variation.

Regarding the liquidity measures, the mean value ofthe Amihud measure is 78.4 bp per million, which indi-cates that trading one million dollars in a particular bondshifts the price by 78.4 bp, on average. The variation inliquidity across bonds is remarkably high and rangesbetween 0.7 and 260.7 bp, a factor of around 400 for the5th and the 95th percentiles. The price dispersion indi-cates the trading cost of a single transaction for which weobserve a mean of around 41.5 bp with high variationacross bonds as well. For the Roll measure, which corre-sponds to the round-trip costs, we observe an averagevalue of 185.1 bp. Interestingly, this mean value is morethan twice as large as the mean value of the pricedispersion measure. Considering the zero-return measure,we find that these are mostly zero, indicating only veryfew observations of stale prices or quotations.

Table 2 presents the correlations between the variousliquidity proxies within our panel data. Overall, we findthe expected patterns: in general, there is positive corre-lation among the trading activity variables (e.g., thecorrelation between volume and number of trades is0.51) and among the liquidity measures estimating trad-ing costs (e.g., the correlation between Amihud, Roll,and price dispersion measure is between 0.02 and 0.2).However, the general level of correlation appears to berelatively low, especially for the liquidity measures. Thus,correlation measured at the individual bond level overtime shows that the liquidity proxies have substantialidiosyncratic movements. This result suggests that the

Table 2This table presents the correlation matrix of bond characteristics (amount issued, coupon, maturity, and age), trading activity variables (traded volume,

number of trades, and time interval between trades), and liquidity measures (Amihud, price dispersion, Roll, and zero-return measure) based on the

panel data for pairwise complete observations. The data set consists of weekly averages of all variables and consists of 23,703 US corporate bonds traded

over the period October 2004 to December 2008.

Amount Coupon Maturity Age Volume Trades Trading Amihud Price Roll Zero-

issued interval dispersion return

Amount issued 1.00

Coupon �0.01 1.00

Maturity �0.05 0.14 1.00

Age �0.12 0.20 �0.03 1.00

Volume 0.46 0.03 0.05 �0.13 1.00

Trades 0.46 �0.02 �0.03 �0.01 0.51 1.00

Trading interval �0.28 �0.02 0.03 0.03 �0.15 �0.17 1.00

Amihud �0.13 �0.01 0.09 0.03 �0.09 �0.07 0.11 1.00

Price dispersion 0.06 0.08 0.28 0.01 0.01 0.14 �0.11 0.02 1.00

Roll �0.29 0.03 0.29 0.08 �0.21 �0.13 0.15 0.19 0.20 1.00

Zero-return �0.04 0.14 �0.01 �0.04 �0.02 �0.06 �0.01 �0.03 �0.01 �0.05 1.00

0

2

4

6

8

10

Spre

ad in

%

Jul 2005 Jul 2006 Jul 2007 Jul 2008

GM/Fordcrisis

Normalperiod

Subprimecrisis

Fig. 2. This figure shows the market-wide corporate bond yield spread

between October 2004 and December 2008 computed by averaging the

bond yield spreads across bonds traded. The corporate bond yield spread

is measured relative to the US Treasury bond yield curve and given in

percentage points. The data set consists of 23,703 US corporate bonds

traded over the period October 2004 to December 2008.


various liquidity proxies are measuring somewhat differ-ent aspects of liquidity empirically, although at a con-ceptual level they are related.10 Therefore, for ourempirical work, the issues of multicollinearity may notbe as severe as one may suspect, at first glance. Note thatonce correlations in our sample are measured at a moreaggregate level (e.g., averaging across time or acrossbonds), the correlations are much higher. Thus, it isimportant not to analyze the bond market based solelyon aggregated data, but also at the level of individualbonds, as we do here, to distinguish between the effects ofthe various liquidity proxies.

To gain a better understanding of the time-seriesbehavior of the bond yield spread over the whole timeperiod, we compute the count-weighted average of thedaily yield spreads over all bonds in our sample.11 Fig. 2shows this time-series of the market-wide average cor-porate bond yield spread, indicating the dramatic increaseof the spread during the two crisis periods. Especiallyduring the subprime crisis, we observe a sharp increase inthe yield spread, which rose, on average, from around 2%to 10%, most likely indicating a far higher risk premiumfor illiquidity and credit risk.

7.2. Liquidity effects in corporate bond yield spreads

In this section, we examine whether liquidity effectsare priced in the US corporate bond market. As argued inSection 3, we expect to find a significant liquidity pre-mium in bond yield spreads. We base our conclusions inthis section on our overall sample covering the wholemarket for the time period of our sample. We present theempirical results explaining the time-series properties ofthe bond yield spread changes with the credit ratings andthe liquidity proxies introduced in Section 5, and using

10 Along the same lines, a principal component analysis (not

reported here) shows that the liquidity proxies can only be represented

by a relatively large number of components.11 We also examine the behavior of bond yield spreads, weighted by

the volume of trading and by the amount outstanding of the individual

bonds, both of which show a similar pattern.

the panel data regression methodology presented inSection 6.

The regressions are based on a sample of data consist-ing of 691,016 bond-week observations. The results areshown in Table 3. This table presents four differentspecifications. In Regression 1, we use a specificationwithout the liquidity proxies, which is a base case thatcan be compared to the other specifications, allowing usto explore the increase in explanatory power after includ-ing liquidity proxies. Note that there is reasonable expla-natory power even in this specification, which includesthe information contained in the dummy variables basedon the credit ratings and the persistence of bond yieldspreads in terms of first differences measured by thelagged term. The next three specifications present theresults of the panel regressions using the liquidity proxies(i.e., trading activity variables and liquidity measures).12

Regression 2 reports the results with the trading activity

12 Since the regressions are based on the change in the bond yield

spread, the static bond characteristics, such as coupon, drop out of the

specification since they are fixed effects. Others, such as age, vary

linearly with time and are absorbed in the constant term.

Table 3This table reports the panel data regression models explaining the yield spread changes based on weekly averages of all variables:

DðYield spreadÞi,t ¼ a0þa1 � DðYield spreadÞi,t�1þa2 � DðVolumeÞi,tþa3 � DðTradesÞi,tþa4 � DðTrading intervalÞi,t

þa5 � DðAmihudÞi,tþa6 �DðPrice dispersionÞi,tþa7 � DðRollÞi,tþa8 � DðZero-returnÞi,tþX21

k ¼ 1

bk � DðRating dummyÞi,t,kþEi,t :

The yield spread change is explained by the change in the lagged yield spread, trading activity variables (traded volume, number of trades, and time

interval between trades), liquidity measures (Amihud, price dispersion, Roll, and zero-return measure), and rating dummies to control for credit risk. The

corporate bond yield spread is measured relative to the US Treasury bond yield curve. In Regression (1) we use a specification without the liquidity

proxies. Regression (2) reports the results with the trading activity variables only, while Regression (3) reports them with the liquidity measures only. In

Regression (4) we add both types of liquidity proxies. The t-statistics are given in parentheses and are calculated from Newey and West (1987) standard

errors, which are corrected for heteroskedasticity and serial correlation. In addition, the table also reports each model’s R2 and the number of

observations. The data set consists of 23,703 US corporate bonds traded over the period October 2004–December 2008.

(1) (2) (3) (4)

Intercept 0.0731nnn 0.0726nnn 0.0721nnn 0.0717nnn

(73.6195) (76.4741) (76.0680) (77.1532)

DðYield spreadÞi,t�1 �0.2853nnn�0.2825nnn

�0.2816nnn�0.2797nnn

(73.6195) (�44.1891) (�43.7139) (�44.0573)

DðVolumeÞi,t �0.0204nnn�0.0108nnn

(�23.2748) (�12.9274)

DðTradesÞi,t 0.0067nnn 0.0054nnn

(16.0245) (12.8891)

DðTrading intervalÞi,t 0.0068nnn 0.0070nnn

(19.4614) (20.2071)

DðAmihudÞi,t 0.0502nnn 0.0477nnn

(35.0938) (33.8126)

DðPrice dispersionÞi,t 0.0744nnn 0.0702nnn

(26.7098) (25.4506)

DðRollÞi,t 0.0510nnn 0.0512nnn

(16.0256) (16.1036)

DðZero-returnÞi,t �0.0774nnn�0.0696nnn

(�8.4762) (�7.6153)

DðRating dummiesÞ Yes Yes Yes Yes

R2 0.0735 0.0766 0.0839 0.0856

Observations 691,016 691,016 691,016 691,016

13 Note that the calculation of the economic significance is based on

the standard deviation of the first differences of the variables. Due to

space limitations we do not report details concerning these statistics for

the first differences.


variables only, while Regression 3 reports them with theliquidity measures only. Regression 4 includes both typesof liquidity proxies.

Focusing on the model that includes both types ofproxies, the results of Regression 4 show that all theliquidity proxies are statistically significant in explainingthe changes in the bond yield spreads. Among the tradingactivity variables, changes in the volume and tradinginterval have the highest t-statistics, while among theliquidity measures, changes in the Amihud measure andthe price dispersion measure are most important. Inter-estingly, despite the correlation across the liquidity mea-sures, they are sufficiently different across bonds and timethat they are all incrementally relevant in explainingthe changes in the bond yield spreads. All variables havethe expected signs except for two liquidity proxies: thenumber of trades and the zero-return measure. Regardingthe zero-return measure, the economic significance of thismeasure is very low, as discussed below. Thus, we assumethat this measure might not be meaningful. As for thenumber of trades, we find that an increase in the numberof trades increases the yield spread. This result can ariseif, in times of crisis, regular trades are split up in smallertrades due to a general reduction in trade size or sellside

pressure, as more institutional orders are broken up to beplaced in the market. This aspect will be analyzed in thenext section.

In terms of R2, we find a relative improvement of about4.2% when the trading activity variables are added toRegression 1. When we add the liquidity measures toRegression 1, we find an additional relative improvementof 9.5% in the R2, showing that liquidity measures aremore important compared to the trading activity vari-ables. Overall, we find that liquidity effects account forapproximately 14% of the explained market-wide corpo-rate yield spread changes.

The Amihud measure turns out to be the most impor-tant explanatory variable in these regressions in economicterms. A one standard deviation change in the Amihudmeasure explains about 6.1 basis points of the change inthe bond yield spread in Regression 4.13 Similar statisticsfor the price dispersion measure and the Roll measure are3.4 bp and 3.1 bp, respectively. The impact of the trading


interval, volume, and number of trades are 2.5, 1.8, and1.5 bp, respectively. The smallest impact is provided bythe zero-return measure (0.8 bp), which seems not to beparticularly relevant given its low economic significance.Considering all liquidity proxies together, a one standarddeviation move in the direction of greater illiquidity in allproxies would increase the yield spread by 19.2 bp. Thiseffect is important when compared with the volatility ofthe yield spread changes of 75.6 bp.14,15

Overall, we find in this analysis that liquidity is animportant factor driving yield spread changes. Liquiditymeasures as well as trading activity variables can explaina fair proportion of bond yield spread changes; in partic-ular, liquidity measures estimating trading costs seem tobe more important than pure trading activity measures.

7.3. Liquidity effects in periods of financial distress

In this section, we explore whether the effect ofliquidity is stronger during times of financial crises. Asargued in Section 3, we expect that liquidity is an evenmore important factor in times of distress. To focus on therole of liquidity in financial crises, we analyze threedifferent subperiods of our overall sample. We presentthe results for the two different crisis periods (the GM/Ford crisis and the subprime crisis) and compare themwith those for the period in between, which can beconsidered as a period with more normal market condi-tions. We first provide evidence on the descriptive statis-tics of the key variables for the three subperiods, and thendraw our main conclusions based on the panel data andFama-MacBeth regressions introduced in Section 6.

The analysis of the averages of the variables in thesethree subperiods allows us to gain some importantinsights into the causes of the variation (see Table 4).The top panel of the table presents the average yield

14 Since credit ratings might adjust slowly compared to changes in

credit risk, part of the explanatory power of the liquidity variables in our

regressions could result because these variables might be proxies for

changes in credit risk. As a robustness check, we test whether adding

future rating changes (i.e., assuming perfect foresight) to the regressions

affects the coefficients of the liquidity variables. In our tests (the results

of which are not reported here to conserve space), we add weekly rating

changes for each of the next 12 weeks to the regression equation in

column 4 of Table 3. We find that future rating changes are statistically

significant, i.e., ratings indeed change slowly. More importantly, how-

ever, we find the same results as in the original regression for the

liquidity variables, i.e., ‘‘perfect-foresight’’ rating information does not

take explanatory power away from the liquidity variables. Thus, our

original results are confirmed and there is no evidence that the liquidity

variables are proxies for credit risk information. Rather, future rating

changes explain part of the current changes in yield spreads, in addition

to changes in the liquidity variables. Furthermore, we test whether the

liquidity variables can forecast future rating changes. Again, we find no

evidence for this conjecture.15 As a robustness check for the use of ratings as a credit risk proxy,

we instead use CDS spreads. We are able to match a small sample

(representing the rather more liquid issues) with 5-year CDS spreads

obtained from Markit. We then repeat our regression analysis using this

CDS spread variable. The R2 is only marginally improved in these

regressions and for our liquidity measures, we find essentially the same

results as in the analysis based on ratings, i.e., the coefficients and

statistical significance stay at the same levels, thus strengthening the

robustness of our results.

spread and the credit rating as well as information aboutthe average daily market-wide trading activity (i.e., num-ber of traded bonds, trades, and volume). The bottompanel provides the liquidity proxies computed for eachsubperiod.

The average yield spread in the normal period of 1.9%is less than in the GM/Ford crisis with 2.3%, and even lessso than in the subprime crisis with 5.0%, documenting thestrong impact of this crisis on yield spreads for the wholemarket. This evidence is also visible in Fig. 2. The averagesof the market-wide trading activity variables are alsoillustrative. During both crises, trading activity is lower,in terms of the number of traded bonds and trade volume,than in the normal period. This reduction is more severein the subprime crisis. For example, the number of bondstraded each day dropped during the subprime crisis, fromroughly 6,000 on average, to a little under 5,200. Thevolume of trading showed a similar decline. Interestingly,during the subprime crisis, we find a larger number oftrades indicating relatively smaller trade sizes for thisperiod. Overall, the impact on trading activity is moresevere in the subprime crisis, indicating that the liquiditychanges that occurred during the two crisis periods weredifferent. During the GM/Ford crisis, there was someshuffling of bond portfolios to account for the shifts incredit ratings, particularly in the automobile sector,resulting only in a minor reduction of trading activity. Incontrast, during the subprime crisis, overall marketliquidity was affected. This point is also evidenced bythe changes in the average credit rating in the differentsubperiods. The credit rating of the average bond tradedduring the GM/Ford crisis was somewhat worse thanduring normal times. In contrast, the credit rating of theaverage bond traded during the subprime crisis wasbetter than during normal times, indicating a flight-to-

quality during the subprime crisis: the average rating is8.8 (close to BBB) for the GM/Ford crisis, 8.4 (between BBBand BBBþ) for the normal period, and 7.6 (between BBBþand A�) for the subprime crisis.

The bottom panel of Table 4 presents similar evidencefor the averages of the daily bond-level liquidity proxies.All liquidity measures indicate lower liquidity in times ofcrisis, especially for the subprime crisis. Considering theaverage price dispersion measure, as one example, we findthat the average value is higher in both crises (46.4 bp inthe GM/Ford crisis and 70.0 bp in the subprime crisis)compared to the normal period (39.8 bp). With regard tothe trading activity variables, we find that the averagedaily volume and the trade interval at the bond-level stayapproximately at the same level. However, the number oftrades increases in both crises. These results are consistentwith the level of market-wide trading activity, where wefind that, in crises, trading takes place in fewer bonds, witha larger number of smaller size trades.

We next analyze the behavior of the changes in theyield spreads in the different subperiods, using the paneldata regression, as in the previous section, incorporatingdummy variables for the subperiods. More importantly,we include interaction terms between the liquidityproxies with the dummy variables for the two crisissubperiods. This setup allows us to analyze whether the

Table 4Panel A shows the mean and standard deviation for the yield spread, credit rating, and daily market-wide trading activity in the three regimes (GM/Ford

crisis, normal period, and subprime crisis). The corporate bond yield spread is measured relative to the US Treasury bond yield curve and given in

percentage points. We use credit ratings from Standard & Poor’s where we assign integer numbers to ratings, i.e., AAA¼1, AAþ¼2, etc., to measure the

average rating. The market-wide trading activity variables represent the number of traded bonds and trades, and the total trading volume per day. Panel

B shows the mean and the standard deviation for the bond characteristics (amount issued, coupon, maturity, and age), trading activity variables (traded

volume, number of trades, and time interval between trades), and liquidity measures (Amihud, price dispersion, Roll, and zero-return measure). The data

set consists of 23,703 US corporate bonds traded over the period October 2004–December 2008.

Panel A: Yield-spread, rating, and market-wide trading activity

Mean Standard deviation

GM/Ford Normal Subprime GM/Ford Normal Subprime

crisis period crisis crisis period crisis

Yield spread (%) 2.34 1.88 5.00 0.43 0.25 2.38

Rating 8.82 8.38 7.63 0.15 0.36 0.28

Traded bonds (thd) 5.23 5.92 5.19 0.54 0.42 0.53

Market-wide trades (thd) 20.43 20.71 22.77 2.34 2.05 4.67

Market-wide volume (bln) 7.65 8.06 6.99 1.32 1.41 1.56

Panel B: Liquidity proxies

Mean Standard deviation

GM/Ford Normal Subprime GM/Ford Normal Subprime

crisis period crisis crisis period crisis

Amount issued (bln) 0.43 0.45 0.54 0.01 0.03 0.06

Coupon (%) 6.26 6.24 6.23 0.06 0.05 0.05

Maturity (yr) 7.57 7.75 8.31 0.13 0.20 0.18

Age (yr) 3.91 4.36 4.76 0.09 0.12 0.14

Volume (mln) 1.51 1.44 1.53 0.26 0.22 0.32

Trades 4.48 4.06 5.33 0.48 0.24 1.31

Trading interval (dy) 3.31 3.38 3.37 0.44 0.49 0.48

Amihud (bp per mln) 66.48 53.21 89.20 6.13 7.42 35.75

Price dispersion (bp) 46.36 39.75 70.02 4.33 1.83 21.84

Roll (bp) 164.28 142.82 209.77 9.57 10.57 52.34

Zero-return (%) 0.02 0.02 0.03 0.01 0.01 0.01

16 Since the t-statistics of the Fama-MacBeth regression could

potentially be biased due to serial correlation, we additionally calculate

results for a cross-sectional regression on time-series averages. This

robustness check (not presented here) shows that the variables are,

again, statistically significant.


yield spread changes are more sensitive to liquiditychanges in times of crisis. The results are presented inTable 5.

Overall, we find that liquidity is far more important intimes of crisis. During the subprime crisis period, we findthat nearly all the liquidity proxies have a statisticallysignificantly higher impact on the changes in the bondyield spreads. Again, this result suggests that the variousliquidity proxies are measuring somewhat different aspectsof liquidity, as already indicated by the low level of corre-lation (see Section 7.1). The most important ones are theprice dispersion and the Amihud measure, where bothcoefficients basically increase by around 100%. A similarresult can be found for the GM/Ford period, although theeffects are not quite as strong. We do not observe a statis-tically significant increase in all of the proxies for theGM/Ford period, and also, the magnitude of the increaseseems to be smaller. However, an F-test shows that we canreject at a 1% level the hypothesis that the interaction termsfor each period of crisis are jointly zero.

In terms of the improvement in R2, we find that theinclusion of the interaction terms leads to an increase from8.56% to 10.14%, compared to the analysis for the wholetime-series, highlighting the importance of adding theseterms. Considering the economic significance, a one stan-dard deviation move in all proxies in the direction of

greater illiquidity would increase the spread by 11.6 bp inthe normal period compared to 15.2 bp and 25.9 bp in theGM/Ford and subprime crisis periods, respectively. Thus,we find a far higher impact of the liquidity proxies in thecrisis periods: the economic significance more than doublesduring the subprime crisis and increases by approximately30% in the GM/Ford crisis. The ranking of the economicimportance of the individual liquidity proxies in the differ-ent time periods stays approximately the same, with theAmihud measure showing the highest impact in all periods(4.3 bp in the normal period, 5.2 bp in the GM/Ford period,and 7.7 bp in the subprime period). In sum, we find asignificant increase, in both statistical and economic terms,of the liquidity component in the crisis periods.

To widen the scope of the analysis, we explore the cross-sectional differences in explaining the bond yield spreadsconsidering all liquidity proxies using the Fama-MacBethprocedure to report the results for the three subperiods.16

Again, rating class dummies are used to explain credit risk-related differences in spreads across bonds.

Table 5This table reports the panel data regression model explaining the yield spread changes based on weekly averages of all variables:

DðYield spreadÞi,t ¼ a0þa1 � DðYield spreadÞi,t�1þa2 � DðVolumeÞi,tþa3 �DðTradesÞi,tþa4 �DðTrading intervalÞi,t

þa5 � DðAmihudÞi,tþa6 � DðPrice dispersionÞi,tþa7 � DðRollÞi,tþa8 � DðZero-returnÞi,tþðGM=Ford dummyÞt � ½b1 � DðYield spreadÞi,t�1

þb2 � DðVolumeÞi,tþb3 � DðTradesÞi,tþb4 � DðTrading intervalÞi,tþb5 �DðAmihudÞi,tþb6 � DðPrice dispersionÞi,t

þb7 � DðRollÞi,tþb8 � DðZero-returnÞi,t �þðSubprime dummyÞt � ½g1 � DðYield spreadÞi,t�1þg2 � DðVolumeÞi,tþg3 � DðTradesÞi,t

þg4 � DðTrading intervalÞi,tþg5 � DðAmihudÞi,tþg6 � DðPrice dispersionÞi,tþg7 � DðRollÞi,tþg8 � DðZero-returnÞi,t �

þX21

k ¼ 1

dk � DðRating dummyÞi,t,kþEi,t :


interval between trades), liquidity measures (Amihud, price dispersion, Roll, and zero-return measure), and rating dummies to control for credit risk.

Additionally, we add interaction terms between the subperiod dummies and the liquidity proxies. The corporate bond yield spread is measured relative

to the US Treasury bond yield curve. The t-statistics are given in parentheses and are calculated from Newey and West (1987) standard errors, which are

corrected for heteroskedasticity and serial correlation. We provide an F-test to test whether the interaction terms of the dummy variable with the

liquidity proxies are jointly zero. The standard errors of the F-statistics are also Newey and West (1987) corrected. In addition, the table also reports the

model’s R2 and the number of observations. The data set consists of 23,703 US corporate bonds traded over the period October 2004–December 2008.

Intercept 0.0644nnn (70.5469)

DðYield spreadÞi,t�1 �0.4318nnn (�47.6400)

DðVolumeÞi,t �0.0137nnn (�15.8406)

DðTradesÞi,t 0.0030nnn (7.3703)

DðTrading intervalÞi,t 0.0032nnn (7.8087)

DðAmihudÞi,t 0.0332nnn (19.7728)

DðPrice dispersionÞi,t 0.0417nnn (13.0552)

DðRollÞi,t 0.0080nnn (2.7972)

DðZero-returnÞi,t �0.0495nnn (�4.5916)

ðGM=Ford dummyÞt �DðYield spreadÞi,t�1 0.0366nnn (3.6263)

ðGM=Ford dummyÞt �DðVolumeÞi,t �0.0028nn (�1.9884)

ðGM=Ford dummyÞt �DðTradesÞi,t 0.0019nnn (2.6333)

ðGM=Ford dummyÞt �DðTrading intervalÞi,t �0.0040nnn (�6.1069)

ðGM=Ford dummyÞt �DðAmihudÞi,t 0.0069nnn (2.6422)

ðGM=Ford dummyÞt �DðPrice dispersionÞi,t 0.0046 (0.9846)

ðGM=Ford dummyÞt �DðRollÞi,t �0.0029 (�0.7340)

ðGM=Ford dummyÞt �DðZero-returnÞi,t 0.0239 (1.3503)

ðSubprime dummyÞt �DðYield spreadÞi,t�1 0.2260nnn (19.5475)

ðSubprime dummyÞt �DðVolumeÞi,t 0.0135nnn (6.5583)

ðSubprime dummyÞt �DðTradesÞi,t 0.0039nnn (4.4352)

ðSubprime dummyÞt �DðTrading intervalÞi,t �0.0070nnn (�8.2507)

ðSubprime dummyÞt �DðAmihudÞi,t 0.0266nnn (9.4860)

ðSubprime dummyÞt �DðPrice dispersionÞi,t 0.0529nnn (9.4447)

ðSubprime dummyÞt �DðRollÞi,t 0.0777nnn (13.6655)

ðSubprime dummyÞt �DðZero-returnÞi,t �0.0824nnn (�3.5895)

DðRating dummiesÞ Yes

F-stat. H0: ðGM=Ford dummyÞ � DðLiquidity proxiesÞ ¼ 0 7.8864

F-stat. H0: ðSubprime dummyÞ � DðLiquidity proxiesÞ ¼ 0 64.3814

Observations 691,016

R2 0.1014


Table 6 provides the detailed results. The findings forthe individual measures basically confirm the resultsof the panel data analysis, i.e., based on the t-statistics,liquidity measures are more important than tradingactivity variables; among the liquidity measures, theAmihud measure and the price dispersion measures arethe most important proxies. As in the panel data analysis,we find an unexpected sign for the number of trades.Interestingly, the bond characteristics are importantliquidity proxies in explaining the cross-section, as well.The most important one is the amount issued with ahigh overall t-statistic. Thus, high outstanding amounts

indicate higher liquidity. The coefficient of the couponvariable indicates higher liquidity for bonds with lowercoupons. As expected, a longer time-to-maturity indicateslower liquidity for bonds in the normal period and inthe GM/Ford crisis. However, the effect is negative forthe subprime period. This result could indicate that, for‘‘buy-and-hold’’ bonds with long maturities, the sellingpressure was not as high as for bonds with shortermaturities resulting in lower spreads.

We find that a large part of the cross-sectional differ-ences in the yield spread across bonds can be explainedby our specification, indicated by an R2 ranging between

Table 6This table reports the cross-sectional regression models explaining the

weekly averages of yield spreads based on the Fama-MacBeth procedure,

estimated for the three regimes (GM/Ford crisis, normal period, and

subprime crisis):

ðYield spreadÞi,t ¼ a0þa1 � ðAmount issuedÞi,tþa2 � ðCouponÞi,t

þa3 � ðMaturityÞi,tþa4 � ðAgeÞi,tþa5 � ðVolumeÞi,t

þa6 � ðTradesÞi,tþa7 � ðTrading intervalÞi,t

þa8 � ðAmihudÞi,tþa9 � ðPrice dispersionÞi,t

þa10 � ðRollÞi,tþa11 � ðZero-returnÞi,t

þX21

k ¼ 1

bk � ðRating dummyÞi,t,kþEi,t :

The level of the yield spread is explained by bond characteristics

(amount issued, coupon, maturity, and age), trading activity variables

(traded volume, number of trades, and time interval between trades),

liquidity measures (Amihud, price dispersion, Roll, and zero-return

measure), and rating dummies to control for credit risk. The corporate

bond yield spread is measured relative to the US Treasury bond yield

curve. The t-statistics are given in parentheses and are calculated from

Newey and West (1987) standard errors, which are corrected for

heteroskedasticity and serial correlation. The table also reports each

model’s R2, and the number of observations, representing the average

number of bonds in the weekly cross-sectional regressions. The data set

consists of 23,703 US corporate bonds traded over the period October

2004–April 2008.

GM/Ford

crisis

Normal

period

Subprime crisis

Intercept 1.8476nnn 1.4437nnn 4.4413nnn

(16.2425) (24.7543) (3.7724)

ðAmount issuedÞi,t �0.2539nnn�0.1824nnn

�0.3250nnn

(�27.2371) (�14.5819) (�10.0361)

ðCouponÞi,t 0.1567nnn 0.1142nnn 0.3506nn

(5.8644) (27.9038) (2.3741)

ðMaturityÞi,t 0.0110nnn 0.0177nnn�0.0599nnn

(3.6594) (11.6510) (�3.6448)

ðAgeÞi,t 0.0053nn�0.0038 �0.0430nnn

(2.4118) (�0.8124) (�3.2945)

ðVolumeÞi,t 0.0013 �0.0113nn 0.0432nn

(0.2851) (�2.4204) (2.4711)

ðTradesÞi,t 0.0452nnn 0.0316nnn 0.0335n

(16.7888) (13.4338) (1.8092)

ðTrading intervalÞi,t 0.0073nnn 0.0025nn 0.0062

(6.0842) (1.9338) (1.0638)

ðAmihudÞi,t 0.0864nnn 0.0718nnn 0.1696nnn

(28.4551) (29.4427) (12.5740)

ðPrice dispersionÞi,t 0.3496nnn 0.2742nnn 0.4523nnn

(14.0045) (18.8816) (7.8913)

ðRollÞi,t 0.0721nnn 0.0808nnn 0.1133n

(8.2594) (23.4407) (1.9265)

ðZero-returnÞi,t 0.2371nnn 0.0387 0.6128

(4.1320) (0.7780) (1.5735)

(Rating dummies) Yes Yes Yes

R2 0.5905 0.6016 0.4966

Observations 3,815 3,845 3,187

17 As a robustness test for causality between liquidity proxies and

yield spreads, we estimated all cross-sectional regressions using liquid-

ity variables lagged by one week instead of contemporaneous ones. We

find that the lagged liquidity proxies show basically the same explana-

tory power as the contemporaneous proxies in the cross-sectional

regressions.


49.7% and 60.2% in the three subperiods. The relativeimprovement in R2 when considering the liquidity proxies(not presented in the tables) is around 10%. Interestingly,this ratio stays at the same level in all three subperiods.Thus, we cannot observe an increase of explanatorypower due to liquidity proxies in the crisis periods. Itseems that especially in the subprime crisis, the spreadlevels of all bonds increased, and thus, the cross-sectionalvariation did not change dramatically. Considering the

credit risk component of the yield spreads, the resultsclearly show the importance of the rating class dummiesin the cross-section, as the remaining 90% of the expla-natory power stems from this credit risk proxy. However,the lower R2 in the subprime crisis results from a decreasein the explanatory power of the credit ratings, indicatingthat ratings could have become stale and reacted ratherslowly to the increase in credit risk.

When analyzing the economic effect, we find that thecross-sectional variation of the yield spread measuredby the standard deviation is 200.5 bp. With regard to theeconomic effect of the liquidity proxies based on theFama-MacBeth regressions, we find statistically signifi-cant results, in terms of the coefficients of the relevantdummy variables: e.g., the Amihud measure and the pricedispersion measure show strong effects; a one standarddeviation change explains around 12.1 bp and 17.1 bp,respectively. The effects are more pronounced in the crisisperiods compared to the normal period, e.g., for the pricedispersion measure, the economic significance is 11.3 bpin the normal period vs. 15.4 bp and 24.4 bp in theGM/Ford and subprime crisis, respectively. Again, thezero-return measure shows the lowest economic effectof around 2.5 bp. A one standard deviation move in all theliquidity proxies in the direction of greater illiquiditywould increase the spread by 98.9 bp in the normalperiod, compared to 111.9 bp and 153.1 bp, respectively,in the GM/Ford and subprime crisis periods. Thus, we finda higher impact of the liquidity proxies in the crisesperiods.17

Overall, the panel data and Fama-MacBeth regressionsshow a significant increase, in both statistical and eco-nomic terms, of the liquidity component in the crisisperiods. We observe a dramatic increase in the liquiditypremium, especially during the subprime crisis. Further-more, we find that beyond liquidity measures and tradingactivity variables, simple bond characteristics, such asthe amount issued, are also of importance in explainingliquidity.

7.4. Interaction effects between liquidity and credit ratings

In this section, we explore whether the effect ofliquidity is related to credit risk measured by creditratings. We divide the bonds into investment grade(AAA to BBB�) and speculative grade (BBþ to C/CCC),expecting the liquidity effects of speculative grade bondsto be more pronounced. This analysis allows us to explorethe interaction between credit and liquidity risk. Weexpect to find lower liquidity effects for investment gradebonds compared to speculative grade bonds, as argued inSection 3.

Fig. 3 shows the yield spreads for the two time-seriesat the market-wide level. As expected, the bond yield


spread for investment grade bonds is always lower thanthat for speculative bonds. However, we stress threeimportant points here: First, the GM/Ford crisis is mainlyreflected in the speculative grade yield spreads, as theGM/Ford bonds were downgraded to junk bond status andprobably had spillover effects in the whole corporatebond market. Second, in the normal period, the differencebetween the spreads of investment and speculative gradebonds systematically shrank over time reflecting decreas-ing risk premiums, a phenomenon that has receivedwidespread attention in the popular press. Third, in the

0

5

10

15

20

25

Spre

ad in

%

Jul 2005 Jul 2006 Jul 2007 Jul 2008

Investment gradeSpeculative grade

Fig. 3. This figure shows the corporate bond yield spread of investment

grade and speculative grade bonds computed by averaging the bond

yield spreads across bonds traded. The corporate bond yield spread is

measured relative to the US Treasury bond yield curve and given in

percentage points. The data set consists of 23,703 US corporate bonds

traded over the period October 2004 to December 2008.

Table 7This table reports the mean of the yield spread, the credit rating, and the d

speculative grade bonds for the three different regimes (GM/Ford crisis, normal p

relative to the US Treasury bond yield curve and given in percentage points.

numbers to ratings, i.e., AAA¼1, AAþ¼2, etc., to measure the average rating. Th

bonds and trades, and the total trading volume per day. Panel B provides the ave

and time interval between trades) and liquidity measures (Amihud, price dispe

corporate bonds traded over the period October 2004–December 2008.

Panel A: Yield-spread, rating, and market-wide trading activity

Investment grade

GM/Ford Normal

crisis period

Yield spread (%) 1.19 0.97

Rating 6.50 6.01

Traded bonds (thd) 3.23 3.90

Market-wide trades (thd) 11.53 13.10

Market-wide volume (bln) 5.26 6.01

Panel B: Liquidity proxies

Investment grade

GM/Ford Normal

crisis period

Volume (mln) 1.99 1.91

Trades 4.37 4.12

Trading interval (dy) 3.28 3.30

Amihud (bp per mln) 61.27 50.47

Price dispersion (bp) 44.74 38.78

Roll (bp) 154.70 128.83

Zero-return (%) 0.01 0.01

subprime crisis, the spread series for both investment andspeculative grade bonds increased dramatically.

Table 7 (Panel A) presents the descriptive statistics of theyield spread, credit rating, and market-wide trading activityfor the two subsegments in the three different time periods.We find that, in general, trading is focused on the invest-ment grade segment. In the GM/Ford crisis, we observe ahigher level of trading activity for the speculative gradesegment compared with the normal period, perhaps dueto the trade volume caused by a shuffling of bonds, due toclientele preferences in anticipation of, and as a conse-quence of, the downgrades. In the subprime crisis, weobserve a lower market-wide volume for both segments.Furthermore, we find a significant reduction in the numberof traded bonds and trades for the speculative grade seg-ment, whereas we observe approximately the same numberof bonds and more trades in the case of investment gradebonds. Thus, we find a flight-to-quality indicated by tradingin better rated bonds compared to the normal period.

Table 7 (Panel B) presents the descriptive statisticsof the liquidity proxies for the two subsegments. Ingeneral, we find that the liquidity proxies clearly indicatelower liquidity for speculative grade bonds, e.g., the pricedispersion measure is 44.1 bp vs. 38.8 bp for investmentgrade bonds in the normal period. In the crisis periods, theliquidity of bonds in both groups deteriorates, e.g., theprice dispersion measure for speculative grade bonds is55.8 bp and 68.2 bp in the GM/Ford and the subprimecrisis, respectively. Interestingly, the difference in theliquidity proxies between the two groups is less

aily market-wide trading activity in Panel A for investment grade and

eriod, and subprime crisis). The corporate bond yield spread is measured

We use credit ratings from Standard & Poor’s where we assign integer

e market-wide trading activity variables represent the number of traded

rages for the trading activity variables (traded volume, number of trades,

rsion, Roll, and zero-return measure). The data set consists of 23,703 US

Speculative grade

Subprime GM/Ford Normal Subprime

crisis crisis period crisis

3.21 4.41 3.48 10.82

5.88 13.10 13.44 14.12

3.96 1.99 2.02 1.22

18.11 8.90 7.61 4.66

5.66 2.38 2.04 1.33

Speculative grade

Subprime GM/Ford Normal Subprime

crisis crisis period crisis

1.77 1.29 0.96 1.08

5.86 4.77 3.94 4.24

3.28 3.18 3.37 3.49

75.14 68.76 54.69 147.94

72.72 55.79 44.09 68.22

206.68 183.47 164.95 215.64

0.01 0.04 0.04 0.06

Table 8This table reports the panel data regression model explaining the yield spread changes based on weekly averages of all variables:

DðYield spreadÞi,t ¼ a0þa1 � DðYield spreadÞi,t�1þa2 � DðVolumeÞi,tþa3 � DðTradesÞi,tþa4 � DðTrading intervalÞi,t

þa5 � DðAmihudÞi,tþa6 �DðPrice dispersionÞi,tþa7 � DðRollÞi,tþa8 � DðZero-returnÞi,tþðSpeculative grade dummyÞt � ½b1 � DðYield spreadÞi,t�1

þb2 � DðVolumeÞi,tþb3 � DðTradesÞi,tþb4 � DðTrading intervalÞi,tþb5 � DðAmihudÞi,tþb6 � DðPrice dispersionÞi,t

þb7 � DðRollÞi,tþb8 � DðZero-returnÞi,t �þX21

k ¼ 1

dk � DðRating dummyÞi,t,kþEi,t :


interval between trades), liquidity measures (Amihud, price dispersion, Roll, and zero-return measure), and rating dummies to control for credit risk.

Additionally, we add interaction terms between the subsegment of speculative grade bonds and the liquidity proxies. The corporate bond yield spread is

measured relative to the US Treasury bond yield curve. The t-statistics are given in parentheses and are calculated from Newey and West (1987) standard

errors, which are corrected for heteroskedasticity and serial correlation. We provide an F-test to test whether the interaction terms of the dummy

variable with the liquidity proxies are jointly zero. The standard errors of the F-statistics are also Newey and West (1987) corrected. In addition, the table

also reports the model’s R2 and the number of observations. The data set consists of 23,703 US corporate bonds traded over the period October 2004–

December 2008.

Intercept 0.0757nnn (73.5243)

DðYield spreadÞi,t�1 �0.3034nnn (�35.2591)

DðVolumeÞi,t �0.0038nnn (�3.6157)

DðTradesÞi,t 0.0057nnn (8.9298)

DðTrading intervalÞi,t 0.0070nnn (15.1603)

DðAmihudÞi,t 0.0458nnn (25.4481)

DðPrice dispersionÞi,t 0.0803nnn (20.8335)

DðRollÞi,t 0.0602nnn (13.5645)

DðZero-returnÞi,t �0.0833nnn (�3.5542)

ðSpeculative grade dummyÞt �DðYield spreadÞi,t�1 0.0377nnn (3.2552)

ðSpeculative grade dummyÞt �DðVolumeÞi,t �0.0122nnn (�4.9216)

ðSpeculative grade dummyÞt �DðTradesÞi,t 0.0015 (1.3913)

ðSpeculative grade dummyÞt �DðTrading intervalÞi,t �0.0097nnn (�9.5900)

ðSpeculative grade dummyÞt �DðAmihudÞi,t 0.0246nnn (7.6564)

ðSpeculative grade dummyÞt �DðPrice dispersionÞi,t 0.0315nnn (4.5624)

ðSpeculative grade dummyÞt �DðRollÞi,t �0.0010 (�0.1301)

ðSpeculative grade dummyÞt �DðZero-returnÞi,t �0.0085 (�0.3184)

DðRating dummiesÞ Yes

F-stat. H0: ðSpeculative grade dummyÞ �DðLiquidity proxiesÞ ¼ 0 28.8800

Observations 637,814

R2 0.0954

18 In other tests, not reported here due to space constraints, we also

estimated a panel data regression separately for each subsegment using


pronounced in the subprime crises for the price disper-sion and Roll measure, i.e., the average trading costincreases relatively more for the investment grade seg-ment. However, for the Amihud measure we find a largedifference between investment and speculative gradebonds in the subprime crisis (i.e., 75.1 bp vs. 147.9 bp)indicating that large trades in speculative grade bondshave a high price impact.

Table 8 presents the results for the panel data regres-sions using a dummy variable for speculative grade bondsand, more important, including interaction terms betweenthis dummy and the liquidity proxies. Overall, we find thatspeculative grade bonds react more strongly to changes inliquidity. The Amihud measure, the price dispersion mea-sure, and the trading activity parameters are significantlyhigher (in absolute terms) for speculative grade bonds.Thus, we find a significant interaction between credit andliquidity risk. On average, bonds with higher credit risk areless liquid and react more strongly to liquidity changes.The most important ones are the Amihud and the pricedispersion measure, for which both coefficients basicallyincrease by 50%. An F-test reveals that we can reject at a

1% level the hypothesis that the interaction terms betweencredit and liquidity risk are jointly zero.

As for the improvement in R2, we find that the inclu-sion of the interaction terms leads to an increase from8.56% to 9.54% compared to the analysis for the wholetime-series, highlighting the importance of adding theseterms. Considering the economic significance, a onestandard deviation move in all proxies in the directionof greater illiquidity would increase the spread by 13.8 bpfor investment grade bonds, compared to 37.6 bp forspeculative grade bonds, respectively. Thus, we find ahigher impact of the liquidity proxies for bonds with highcredit risk. The ranking of the economic importance of theindividual liquidity proxies for investment grade andspeculative grade bonds stays approximately the same,with the Amihud measure showing the highest impact(4.6 bp for investment grade bonds and 10.4 bp for spec-ulative grade bonds).18


Overall, we find that the liquidity effects are far morepronounced for speculative grade bonds and, thus, indi-cating an interaction between credit and liquidity risk.This effect is particularly important for the subprimecrisis, when we observe a clear flight-to-quality effect.

8. Conclusion

Financial economists have been concerned with theimpact of liquidity and liquidity risk on the pricing ofassets for at least two decades. During this period, severalissues relating to liquidity effects in asset prices havebeen analyzed at a theoretical and empirical level byacademic researchers, particularly in the context of USequity markets. More recently, the focus on liquidity hasbeen broadened to include a wider class of assets such asderivatives and fixed income securities. This trend hasaccelerated since the onset of the subprime crisis, as thediscussion of liquidity has attracted much interest amongacademics, practitioners, and regulators. While the crisishas manifested itself in almost every financial market inthe world, the most stressed markets, by far, have beenthose for fixed income securities and their derivatives,particularly those with credit risk, including corporatebonds, CDSs, and CDOs. These developments require thatthe scope of the discussion of liquidity be extended toinclude the interplay between liquidity and credit.

Corporate bond markets are far less liquid than relatedequity markets, since only a very small proportion of theuniverse of corporate bonds trades even as often as once aday. In addition, corporate bonds trade in an over-the-counter market, where there is no central market place.Hence, conventional transaction metrics of liquidity such asbid-offer quotes do not have the same meaning in thismarket compared to exchange traded markets. The issue ofliquidity in this relatively illiquid, OTC market is fundamen-tally different from that in exchange traded markets: Thus,it is necessary to use measures of liquidity that go beyondthe standard transaction-based measures common inresearch in more liquid, exchange traded markets.

We employ a wide range of liquidity measures toquantify the liquidity effects in corporate bond yieldspreads. Our analysis explores the time-series and cross-sectional aspects of liquidity using panel and Fama-MacBeth regressions, respectively. We find that theliquidity proxies in the specified regression modelsaccount for about 14% of the explained time-series varia-tion of the yield spread changes. Furthermore, we findthat the effect of the liquidity measures is far stronger inboth the GM/Ford crisis and the subprime crisis, mostremarkably the economic effect more than doubles in thesubprime crisis. All the liquidity proxies considered exhi-bit statistically as well as economically significant results.

(footnote continued)

dummy variables with interaction terms for the subperiods. This allows

us to compare liquidity effects in different time periods between the

investment grade and speculative grade bonds. For the subprime crisis,

we find a significant increase in the liquidity proxies for both subseg-

ments, where the increase is particularly strong for speculative grade

bonds. This result reinforces the findings of the previous analysis.

In particular, measures estimating trading costs based ontransaction data show the strongest effects.

Comparing investment grade to speculative gradebonds, we find lower liquidity for speculative grade bondsas well as a stronger reaction to changes in liquidity.These results show that bonds with higher credit risk alsoare more exposed to liquidity risk.

These results are useful for many practical applica-tions, particularly pricing and risk management, and alsohave implications for regulatory policy. They also high-light the importance of transparency of trades for OTCmarkets, with reporting to a central authority being acrucial element for price discovery.

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